What are the causes of pain in the back and down the leg?

A pinched nerve. Decreased space for the nerves in the low back can results in low back pain that radiates into the lower extremities. This can be due to a herniated disc, spinal stenosis, spondylolisthesis, or a variety of other reasons (including hip arthritis, poor circulation, etc.).
Several things . Including a disc herniation. There are other possibilities. Peripheral vascular disease & spinal stenosis both can cause pain into a leg mimicking sciatic pain as can other issues like hip & knee arthritis. Other causes of nerve compression in the spine due to a tumor, infection or fracture can cause this pain. Pyriformis syndrome can also cause radiating leg pain as can sacroiliac joint issues.